Proof.Tactical

introv

introv is used to name only non-dependent hypothesis.

If introv is called on a goal of the form forall x, H, it should introduce all the variables quantified with a forall at the head of the goal, but it does not introduce hypotheses that preceed an arrow constructor, like in P -> Q.
If introv is called on a goal that is not of the form forall x, H nor P -> Q, the tactic unfolds definitions until the goal takes the form forall x, H or P -> Q. If unfolding definitions does not produces a goal of this form, then the tactic introv does nothing at all.

(* introv_rec introduces all visible variables.
   It does not try to unfold any definition. *)

Ltac introv_rec :=
  match goal with
  | |- ?P -> ?Q => idtac
  | |- forall _, _ => intro; introv_rec
  | |- _ => idtac
  end.

(* introv_noarg forces the goal to be a forall or an ->,
   and then calls introv_rec to introduces variables
   (possibly none, in which case introv is the same as hnf).
   If the goal is not a product, then it does not do anything. *)

Ltac introv_noarg :=
  match goal with
  | |- ?P -> ?Q => idtac
  | |- forall _, _ => introv_rec
  | |- ?G => hnf;
     match goal with
     | |- ?P -> ?Q => idtac
     | |- forall _, _ => introv_rec
     end
  | |- _ => idtac
  end.

  (* simpler yet perhaps less efficient imlementation *)
  Ltac introv_noarg_not_optimized :=
    intro; match goal with H:_|-_ => revert H end; introv_rec.

(* introv_arg H introduces one non-dependent hypothesis
   under the name H, after introducing the variables
   quantified with a forall that preceeds this hypothesis.
   This tactic fails if there does not exist a hypothesis
   to be introduced. *)
  (* todo: __ in introv means "intros" *)

Ltac introv_arg H :=
  hnf; match goal with
  | |- ?P -> ?Q => intros H
  | |- forall _, _ => intro; introv_arg H
  end.

(* introv I1 .. IN iterates introv Ik *)

Tactic Notation "introv" :=
  introv_noarg.
Tactic Notation "introv" simple_intropattern(I1) :=
  introv_arg I1.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2) :=
  introv I1; introv I2.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) :=
  introv I1; introv I2 I3.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) :=
  introv I1; introv I2 I3 I4.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) simple_intropattern(I5) :=
  introv I1; introv I2 I3 I4 I5.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) simple_intropattern(I5)
simple_intropattern(I6) :=
  introv I1; introv I2 I3 I4 I5 I6.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) simple_intropattern(I5)
simple_intropattern(I6) simple_intropattern(I7) :=
  introv I1; introv I2 I3 I4 I5 I6 I7.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) simple_intropattern(I5)
simple_intropattern(I6) simple_intropattern(I7) simple_intropattern(I8) :=
  introv I1; introv I2 I3 I4 I5 I6 I7 I8.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) simple_intropattern(I5)
simple_intropattern(I6) simple_intropattern(I7) simple_intropattern(I8)
simple_intropattern(I9) :=
  introv I1; introv I2 I3 I4 I5 I6 I7 I8 I9.
Tactic Notation "introv" simple_intropattern(I1) simple_intropattern(I2)
simple_intropattern(I3) simple_intropattern(I4) simple_intropattern(I5)
simple_intropattern(I6) simple_intropattern(I7) simple_intropattern(I8)
simple_intropattern(I9) simple_intropattern(I10) :=
  introv I1; introv I2 I3 I4 I5 I6 I7 I8 I9 I10.

gen

Tactic Notation "gen" ident(X1) :=
  generalize dependent X1.
Tactic Notation "gen" ident(X1) ident(X2) :=
  gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) :=
  gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) :=
  gen X4; gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) ident(X5) :=
  gen X5; gen X4; gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) ident(X5)
ident(X6) :=
  gen X6; gen X5; gen X4; gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) ident(X5)
ident(X6) ident(X7) :=
  gen X7; gen X6; gen X5; gen X4; gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) ident(X5)
ident(X6) ident(X7) ident(X8) :=
  gen X8; gen X7; gen X6; gen X5; gen X4; gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) ident(X5)
ident(X6) ident(X7) ident(X8) ident(X9) :=
  gen X9; gen X8; gen X7; gen X6; gen X5; gen X4; gen X3; gen X2; gen X1.
Tactic Notation "gen" ident(X1) ident(X2) ident(X3) ident(X4) ident(X5)
ident(X6) ident(X7) ident(X8) ident(X9) ident(X10) :=
  gen X10; gen X9; gen X8; gen X7; gen X6; gen X5; gen X4; gen X3; gen X2; gen X1.

exploit

Lemma modusponens: forall (P Q: Prop), P -> (P -> Q ) -> Q.
Proof. auto. Qed.

Ltac exploit x :=
refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
|| refine (modusponens _ _ (x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _) _)
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